A wide variety of tomography apparatus and methods are known, including systems based on electrical impedance tomography (EIT) and electrical resistance tomography (ERT). It is also known to use such apparatus and methods for generating tomograms (e.g. conductivity profiles of cross sections of samples) of substantially stationary samples and also for moving the samples, for example flowing samples in a pipe or other conduit, such as liquids, solids, gases or any combination or mixture thereof. In such applications an array of electrodes is typically arranged around the perimeter of a sample-containing volume, such that each electrode is in electrical contact with the sample. The apparatus then comprises measurement means which is adapted to perform a set of measurements on the sample, each measurement comprising the passing of a current through the sample using a pair of the electrodes, and measuring a resultant voltage developed across a different pair of the electrodes. In general, the larger the number of electrodes and the larger the number of different measurements made using those electrodes, the higher the resolution of the tomogram that can be calculated from the measurements. The apparatus typically comprises processing means adapted to calculate a tomogram representing the conductivity of the sample as a function of position on the cross section surrounded by the electrodes from the complete set of measurement results. The apparatus may also comprise display means adapted to display the calculated tomogram. The tomogram may comprise a plurality of pixels. The mathematical/processing techniques for generating tomograms from the measurement results/data are well known in the prior art, and will be apparent to the person skilled in this field.
In certain known tomography apparatus, 16 electrodes are equally spaced around a circular perimeter of a sample-containing volume, and the measurement means is adapted to take a set of measurements using the so-called “adjacent pair” technique. In the adjacent-pair method, each measurement comprises passing a current through the sample using one adjacent pair of electrodes, and measuring a resultant voltage developed across a different adjacent pair of electrodes. It is known for the data set to comprise 104 such measurements for an array of 16 electrodes, with this set comprising 8 sub-sets (or alternatively 16 sub-sets—see below), each sub-set using a different adjacent pair of electrodes to pass current through the sample and no electrode being used in more than one pair of exciting/current-driving pairs. Then, in each sub-set, with the selected adjacent pair of electrodes driving current through the sample, 13 different voltage measurements are made using the full set of different adjacent pairs of remaining electrodes (i.e. the electrodes other than the pair selected to drive current). For example, in a first sub-set, electrodes 1 and 2 may be used to drive current through the sample. Then, voltage measurements are taken between electrodes 3 and 4, 4 and 5, 5 and 6, etc. up to the final voltage measurement between electrodes 15 and 16. Thus, the electrodes 1 and 2 being used in this sub-set to drive current are not used in any of the corresponding voltage measurements, thereby avoiding any problems associated with electrode to sample impedances. Also, it is known for the initial data set obtained from an array of 16 electrodes to comprise 16 subsets, with a total of 256 measurements initially being made. Then, only 104 measurements may be used as independent measurements, by removing those measurements obtained from electrodes involved with current injection and measurements as the mutual same based on the reciprocity theory in electrical impedance measurement. These are determined by N=(Ne−3)Ne/2 or 104=(16−3)16/2 (where Ne is the number of electrodes).
Whilst this known technique of deriving a tomogram from 104 measurements, or an even greater number, made using the set of 16 electrodes is able to produce tomograms with useful resolution, it will be appreciated that the amount of processing required to produce the tomogram is large. This places high demands on the processing apparatus required, and in general, of course, for a given processing capacity the larger the number of measurements and resultant processing operations to be performed to produce the tomogram, the longer the time taken to produce the tomogram.